I've done some simple measurements with one of these 10ohm 0805 resistors, and with a 1.5v AA battery I'm getting a draw of about 180mA
But even simpler maths will show that you actually have a current of 150mA (it's called Ohm's law).
When you mention MOSFET options, you mean buying beefier transistor arrays, right?
No MOSFETS are a completely different device. I used them in this project to drive my 8 X 8 matrix. You can do the same just replace the LEDs with resistors and omit the switches and diodes.
http://www.thebox.myzen.co.uk/Hardware/Econo_Monome.html